Boundary One-Point Functions in the Open XXZ Spin Chain with Generic Integrable Boundaries
Till Bargheer, Tengis Batmunkh, Paul Ryan
We consider the problem of computing observables beyond the spectrum in the open XXZ spin chain with the most generic integrable boundary conditions. For such boundaries, the residual u(1) symmetry is broken and the familiar Baxter TQ equation describing the spectrum becomes inhomogeneous, placing the model outside the realm of existing approaches to correlation functions and form factors. We show that the Functional Separation of Variables method, so far developed mainly for rational, (quasi-)periodic spin chains, is largely insensitive to these modifications, and works equally well for diagonal and generic boundaries. Using this method, we compute exact determinant expressions for a prototypical example of form factors in open-boundary systems, namely the longitudinal and transverse boundary-spin one-point functions in arbitrary Hamiltonian eigenstates at finite system size. No constraint relating the two boundary configurations and no reference state are required. We verify the resulting formulae against direct finite-volume diagonalisation.
arXiv:2610.27062•Oct 19, 2026•0 citations